(2a-5)(3a+1)=

Solution for (2a-5)(3a+1)= equation:

Simplifying
(2a + -5)(3a + 1) = 0

Reorder the terms:
(-5 + 2a)(3a + 1) = 0

Reorder the terms:
(-5 + 2a)(1 + 3a) = 0

Multiply (-5 + 2a) * (1 + 3a)
(-5(1 + 3a) + 2a * (1 + 3a)) = 0
((1 * -5 + 3a * -5) + 2a * (1 + 3a)) = 0
((-5 + -15a) + 2a * (1 + 3a)) = 0
(-5 + -15a + (1 * 2a + 3a * 2a)) = 0
(-5 + -15a + (2a + 6a2)) = 0

Combine like terms: -15a + 2a = -13a
(-5 + -13a + 6a2) = 0

Solving
-5 + -13a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -3a)(5 + -2a) = 0

Subproblem 1
Set the factor '(-1 + -3a)' equal to zero and attempt to solve:

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -3a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1

Combine like terms: 0 + 1 = 1
-3a = 1

Divide each side by '-3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-0.3333333333, 2.5}